Two-stage combining and beamforming for FDD massive MIMO relay system with user-pair scheduling

This paper proposes a novel two-stage combining and beamforming with user-pair scheduling (TSCBUS) scheme to address the core challenges of excessive pilot overhead in frequency division duplexing massive MIMO relay systems. Unlike existing schemes, the proposed TSCBUS scheme leverages statistical channel state information to jointly design the pre-combining and pre-beamforming matrices (PPMs) with user-pair scheduling, reducing pilot overhead while improving effective spectral efficiency (ESE). Specifically, in the first stage, the PPMs design and user-pair scheduling problem is formulated as a multivariable optimization problem with the goal of maximizing the received energy and the constraints of a limited number of radio frequency (RF) chains, a limited number of orthogonal pilots, and maximum available serving user-pairs. Then, a graph-based iterative optimization with user-pair scheduling (G-IOUS) algorithm is proposed to solve the formulated problem. In the G-IOUS algorithm, user-pair scheduling is performed via a greedy algorithm, where the user-pair with the largest received energy in the unscheduled user-pairs set is selected in each iteration. To get the received energy of each unscheduled user-pair in each iteration of the G-IOUS algorithm, the PPMs are required to be determined and the PPMs design problem is transformed into three sub-problems and solved using an alternative optimization manner, involving the pre-combining matrix design, the pre-beamforming matrix design, and an intermediate matrix design. Using the graph theory to obtain the pilot overhead, the sub-problems of the PPMs design are converted into 0-1 integer programming problems for solving, and the intermediate matrix is designed through convex programming. This process generates significantly reduced-dimension, well-conditioned equivalent channel matrices that ensure feasibility under RF chain constraints and enable low-overhead channel estimation and feedback. In the second stage, a zero-forcing-based digital precoder is designed based on the estimated reduced-dimension instantaneous equivalent channel state information to enhance the ESE through multi-user interference suppression. Simulation results verify that our proposed scheme outperforms the other schemes in improving the ESE.